Computer-aided design (CAD) software allows a user to construct and manipulate complex three-dimensional (3D) models. A number of different modeling techniques can be used to create a 3D model. One such technique is a solid modeling technique, which provides for topological 3D models where the 3D model is a collection of interconnected topological entities (e.g., vertices, edges, and faces). The topological entities have corresponding supporting geometrical entities (e.g., points, trimmed curves, and trimmed surfaces). The trimmed surfaces correspond to the topological faces bounded by the edges. CAD systems may combine solid modeling and other modeling techniques, such as parametric modeling techniques. Parametric modeling techniques can be used to define various parameters for different features and components of a model, and to define relationships between those features and components based on relationships between the various parameters.
A design engineer is a typical user of a 3D CAD system. The design engineer designs physical and aesthetic aspects of 3D models, and is skilled in 3D modeling techniques. The design engineer creates parts and may assemble the parts into a subassembly. Parts and subassemblies may then be used to design an assembly. Additionally, a design engineer may wish to run a simulation in order to better analyze the design of a subassembly or an assembly model. Analyzing simulation results can give a design engineer valuable information about kinematic and dynamic responses of the model, by way of non-limiting example. With the ability to simulate an assembly before the assembly is manufactured, the design engineer can test the design virtually without incurring the overhead associated with the manufacturing process. Virtually testing a design before manufacturing physical parts can lead to considerable cost and time savings because the product design can be tested before the actual product is manufactured and various design changes can be tested quickly and effectively. Commercially available modeling and simulation systems include the SolidWorks® 2011 software and SolidWorks® 2011 Simulation systems available from Dassault Systèmes SolidWorks Corporation of Concord, Mass.
When designing an assembly containing a motor, a design engineer may want to compute the reflected mass or reflected inertia of the assembly. Reflected mass (sometimes referred to as reflected load mass) is the mass of an entire mechanism sensed by a linear motor at the motor drive shaft. Reflected inertia (sometimes referred to as reflected load inertia) is the inertia of an entire mechanism sensed by a rotary motor at the motor drive shaft. Reflected mass and reflected inertia data aids the design engineer in determining whether the selected motor is the most efficient and cost effective for the real-world mechanism being designed. Current methods for computing reflected mass and reflected inertia use manual calculations and the results may be approximate because dynamic effects such as the time rate of change of reflected mass or reflected inertia (i.e., the rate in which reflected mass or reflected inertia changes with respect to time), are not taken into account, and thus, the results are not always accurate. Further, current methods compute reflected mass and reflected inertia of a mechanism at a specific motor location and only in a specific configuration in which various parts are frozen in time. Thus, such a computation is valid only for a specific position of the mechanism and cannot easily provide the time variation at all possible configurations (positions) of the mechanism. To obtain results via a manual computation procedure is very tedious and can quickly become very difficult for a moderately complex mechanism.
Selecting a proper motor that drives a mechanism for a particular task is a critical task during the design phase of the mechanism in terms of efficiency, cost, and performance. With regards to efficiency, selecting a higher capacity motor than needed results in the motor being under-utilized, thereby leading to higher power consumption than necessary and other inefficiencies, for example, higher cost to purchase and install the motor, higher operating costs, and a bulkier design. On the other hand, selecting a lower capacity motor than needed may lead to the motor overheating, being unable to perform the desired task, or breaking down. With regards to costs, ensuring that a selected motor is not larger and more expensive than needed helps control costs of a product. Performance is also a prime consideration when selecting a motor. If a motor does not have the proper inertia there will be a mismatch of motor inertia and load inertia, and mismatched inertia may lead to unacceptable vibrations of the mechanism. In addition, “inertia mismatches require higher current to drive the motor, thus [dissipating] more power,” according to John Mazurkiewicz in a paper titled Load Inertia and Motor Selection (see www.motioncontrolonline.org/files/public/Load_Inertia_Motor_Selection.pdf).
Usually, reflected mass and reflected inertia are computed using a static snapshot of the mechanism that considers the loading conditions at one particular instant in time. Moreover, the reflected mass and reflected inertia computations depend upon how various parts in the mechanism are coupled, and as mentioned, are usually computed manually. Effects of other forces such as friction, gravity, and external loads are usually accounted for in an approximate fashion, for example, by reflecting external loads across the transmission system with a known transmission ratio. However, when the path from the external load to the motor involves complicated chains of linkages and joints, such a process is neither easy nor obvious. Thus, the manual computations are seldom exact. As the mechanism actuates, positions of different parts change and internal and external loads on the mechanism change as well. All of these affect reflected mass in the case of a linear motor and reflected inertia in the case of a rotary motor, in a very complex fashion. Therefore, manually computing reflected mass and reflected inertia at every position to find a motor's time variation is by and large a very tedious and difficult task.
Time-saving advantages and enhancements to state of the art CAD systems could be achieved by providing an efficient and more accurate means of computing reflected mass and reflected inertia of computer-aided design models containing motors.